The Police had the Joker surrounded, he threatened the hospital and then they all left, as opposed to going in and arresting him.

What scene are you talking about? The Police didn't have him surrounded. They were all tied up evacuating the hospitals across Gotham and protecting Reese from the rampaging Gothamites.

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Another scene that makes no sense is when Batman saves Rachel from being thrown out the window. The two of them are completely relaxed even though the Joker was still up there (at least as far as they knew).

Batman hid Dent and then took out all of Joker's men. Joker was alone and would not be sticking around to ask the guests again where Harvey was.

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